Boxicity and separation dimension

Manu Basavaraju; L. Sunil Chandran; Martin Charles Golumbic; Rogers Mathew; Deepak Rajendraprasad

doi:10.1007/978-3-319-12340-0_7

Boxicity and separation dimension

Manu Basavaraju, L. Sunil Chandran, Martin Charles Golumbic, Rogers Mathew, Deepak Rajendraprasad

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A family F of permutations of the vertices of a hypergraph H is called pairwise suitable for H if, for every pair of disjoint edges in H, there exists a permutation in F in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for H is called the separation dimension of H and is denoted by π(H). Equivalently, π(H) is the smallest natural number k so that the vertices of H can be embedded in ℝ^k such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph H is equal to the boxicity of the line graph of H. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension.

Original language	English
Title of host publication	Graph-Theoretic Concepts in Computer Science - 40th International Workshop, WG 2014, Revised Selected Papers
Editors	Dieter Kratsch, Ioan Todinca
Publisher	Springer Verlag
Pages	81-92
Number of pages	12
ISBN (Electronic)	9783319123394
DOIs	https://doi.org/10.1007/978-3-319-12340-0_7
State	Published - 2014
Event	40th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2014 - Orléans, France Duration: 25 Jun 2014 → 27 Jun 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8747
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	40th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2014
Country/Territory	France
City	Orléans
Period	25/06/14 → 27/06/14

Bibliographical note

Funding Information:
Rogers Mathew and Deepak Rajendraprasad: Supported by VATAT Postdoctoral Fellowship, Council of Higher Education, Israel.

Funding Information:
Manu Basavaraju: Supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement n. 267959.

Publisher Copyright:
© Springer International Publishing Switzerland 2014.

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)

Access to Document

10.1007/978-3-319-12340-0_7

Cite this

Basavaraju, M., Sunil Chandran, L., Golumbic, M. C., Mathew, R., & Rajendraprasad, D. (2014). Boxicity and separation dimension. In D. Kratsch, & I. Todinca (Eds.), Graph-Theoretic Concepts in Computer Science - 40th International Workshop, WG 2014, Revised Selected Papers (pp. 81-92). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8747). Springer Verlag. https://doi.org/10.1007/978-3-319-12340-0_7

Basavaraju, Manu ; Sunil Chandran, L. ; Golumbic, Martin Charles et al. / Boxicity and separation dimension. Graph-Theoretic Concepts in Computer Science - 40th International Workshop, WG 2014, Revised Selected Papers. editor / Dieter Kratsch ; Ioan Todinca. Springer Verlag, 2014. pp. 81-92 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "A family F of permutations of the vertices of a hypergraph H is called pairwise suitable for H if, for every pair of disjoint edges in H, there exists a permutation in F in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for H is called the separation dimension of H and is denoted by π(H). Equivalently, π(H) is the smallest natural number k so that the vertices of H can be embedded in ℝk such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph H is equal to the boxicity of the line graph of H. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension.",

author = "Manu Basavaraju and {Sunil Chandran}, L. and Golumbic, {Martin Charles} and Rogers Mathew and Deepak Rajendraprasad",

note = "Funding Information: Rogers Mathew and Deepak Rajendraprasad: Supported by VATAT Postdoctoral Fellowship, Council of Higher Education, Israel. Funding Information: Manu Basavaraju: Supported by the European Research Council under the European Union{\textquoteright}s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement n. 267959. Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2014.; 40th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2014 ; Conference date: 25-06-2014 Through 27-06-2014",

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Basavaraju, M, Sunil Chandran, L, Golumbic, MC, Mathew, R & Rajendraprasad, D 2014, Boxicity and separation dimension. in D Kratsch & I Todinca (eds), Graph-Theoretic Concepts in Computer Science - 40th International Workshop, WG 2014, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8747, Springer Verlag, pp. 81-92, 40th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2014, Orléans, France, 25/06/14. https://doi.org/10.1007/978-3-319-12340-0_7

Boxicity and separation dimension. / Basavaraju, Manu; Sunil Chandran, L.; Golumbic, Martin Charles et al.

Graph-Theoretic Concepts in Computer Science - 40th International Workshop, WG 2014, Revised Selected Papers. ed. / Dieter Kratsch; Ioan Todinca. Springer Verlag, 2014. p. 81-92 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8747).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N1 - Funding Information: Rogers Mathew and Deepak Rajendraprasad: Supported by VATAT Postdoctoral Fellowship, Council of Higher Education, Israel. Funding Information: Manu Basavaraju: Supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement n. 267959. Publisher Copyright: © Springer International Publishing Switzerland 2014.

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N2 - A family F of permutations of the vertices of a hypergraph H is called pairwise suitable for H if, for every pair of disjoint edges in H, there exists a permutation in F in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for H is called the separation dimension of H and is denoted by π(H). Equivalently, π(H) is the smallest natural number k so that the vertices of H can be embedded in ℝk such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph H is equal to the boxicity of the line graph of H. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension.

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Basavaraju M, Sunil Chandran L, Golumbic MC, Mathew R, Rajendraprasad D. Boxicity and separation dimension. In Kratsch D, Todinca I, editors, Graph-Theoretic Concepts in Computer Science - 40th International Workshop, WG 2014, Revised Selected Papers. Springer Verlag. 2014. p. 81-92. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-12340-0_7

Boxicity and separation dimension

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